A Stochastic Analysis of Table Tennis

TL;DR

This paper develops a probabilistic model for scoring in table tennis, analyzing how game parameters and rule changes affect match dynamics and providing tools for assessing player skills.

Contribution

It introduces a general formula for the score distribution in table tennis and explores the impact of rule changes on game statistics and player ability estimation.

Findings

Derived the distribution, expectation, and variance of rallies needed for specific scores.

Analyzed the effect of rule changes on game dynamics and scoring.

Suggested methods for estimating individual player abilities.

Abstract

We establish a general formula for the distribution of the score in table tennis. We use this formula to derive the probability distribution (and hence the expectation and variance) of the number of rallies necessary to achieve any given score. We use these findings to investigate the dependence of these quantities on the different parameters involved (number of points needed to win a set, number of consecutive serves, etc.), with particular focus on the rule change imposed in 2001 by the International Table Tennis Federation (ITTF). Finally we briefly indicate how our results can lead to more efficient estimation techniques of individual players' abilities.